1. Field of the Invention
The present invention generally concerns magnetic resonance tomography (MRT) as used in medicine for examination of patients. The present invention particularly concerns a method as well as a magnetic resonance tomography apparatus for implementation of such a method in which two-dimensional or three-dimensional sensitivity-encoded magnetic resonance imaging using an acquisition coil array for partially parallel acquisition (PPA) is employed for completion of under-sampled magnetic resonance data sets.
2. Description of the Prior Art
MRT is based on the physical phenomenon of nuclear magnetic resonance and has been successfully used as an imaging method for over 20 years in medicine and biophysics. In this examination modality the subject is exposed to a strong, constant magnetic field. The nuclear spins of the atoms in the subject, which were previously randomly oriented, thereby align. Radio-frequency energy can now excite these “ordered” nuclear spins to a specific oscillation. In MRT, this oscillation generates the actual measurement signal which is acquired by means of suitable reception coils. Non-homogeneous magnetic fields generated by gradient coils follow the measurement subject to be spatially coded in all three spatial directions. The method allows a free selection of the slice to be imaged, so slice images of the human body can be acquired in all directions. MRT as a slice imaging method in medical diagnostics is distinguished predominantly as a non-invasive examination method with a versatile contrast capability. Due to the excellent representation capability of soft tissue, MRT has developed into a method superior in many ways to x-ray computed tomography (CT). MRT today is based on the application of spin echo and gradient echo sequences that enable an excellent image quality with measurement times on the order of minutes.
The continuous technical development of the components of MRT apparatuses and the introduction of faster imaging sequences has opened more fields of use for MRT in medicine. Real-time imaging for supporting minimally-invasive surgery, functional imaging in neurology, and perfusion measurement in cardiology are only a few examples. In spite of the technical advances in the design of MRT apparatuses, the acquisition time of an MRT image remains the limiting factor for many applications of MRT in medical diagnostics. From a technical viewpoint (feasibility) and for reasons of patient protocol (stimulation and tissue heating), a limit is set on a further increase of the performance of MRT apparatuses with regard to the acquisition time. In recent years numerous efforts have therefore been made to further reduce the image measurement time.
One approach to shorten the acquisition time is to reduce the number of the measurement steps. In order to obtain a complete image from such a data set, either the missing data must be reconstructed with suitable algorithms or the incorrect image from the reduced data must be corrected.
The acquisition of the data in MRT occurs in a mathematical organization known as k-space (frequency domain). The MRT image in what is known as the image domain is linked with the MRT data in k-space by means of Fourier transformation. The spatial coding of the subject who spans k-space can ensue in various ways. A Cartesian sampling (i.e. a sampling in the form of straight parallel lines) or a per-projection sampling (i.e. a sampling running linearly through the k-space center) are most conventional. An arbitrary three-dimensional sampling is also possible, wherein the trajectories along which the sampling ensues can have arbitrary shape (for example spiral form, linear segments, propeller shape, etc.) and do not necessary have to intersect the k-space center. The coding generally ensues by means of gradients in all three spatial directions. Given Cartesian sampling, differentiation is made between the slice selection (establishes an acquisition slice in the subject, for example the z-axis), the frequency coding (establishes a direction in the slice, for example the x-axis) and the phase coding (determines the second dimension within the slice, for example the y-axis).
The acquisition method for projection reconstruction is a simple variant in which a gradient is used that is not successively increased and thus does not scan line-by-line in the Cartesian format, but rather is rotated around the sample. In each measurement step a projection is thus acquired from a specific direction through the entire sample, and thus a typical data set for the projection reconstruction in k-space as is, for example, presented in FIG. 4 by the projections (A), (B), (D) and (E). The entirety of the points corresponding to the acquired data in k-space is called a projection data set.
In a general three-dimensional acquisition method a suitable gradient switching can effect the scanning along different trajectories whose path (as noted) does not necessarily need to intersect the k-space center and which do not need to be geometrically correlated either in parallel or in any manner at all.
In contrast to Cartesian scanning, radial (or spiral) scanning of the frequency domain is advantageous particularly for the imaging moving subjects (such as the beating heart) because movement artifacts smear over the entire image field in the image reconstruction and thus do not obscure pathological findings. In Cartesian scanning of the frequency domain, interfering ghost images occur in the reconstructed image that usually appear as periodically repeating image structures in the phase coding direction. The longer (in comparison to Cartesian scanning) measurement time that is required for nominally equal spatial resolution is disadvantageous in the case of a non-Cartesian radial, spiral or arbitrary further two- or three-dimensional scanning of the frequency domain. In Cartesian scanning, the number of the phase coding steps Nγ (for example the number of the angle steps Nφ (the additional angle steps Nψ in 3D) given radial scanning) determines the measurement time. For the same spatial resolution,
      N    ϕ    =            π      2        ⁢                  N        y            .      
Most PPA methods for shortening the image measurement time in the case of Cartesian scanning are based on a reduction of the number of time-consuming phase coding steps Nγ and the use of a number of signal acquisition coils, known as “partially parallel acquisition” and designated as PPA. The transfer of this principle to data acquisition methods with radial (2D or 3D) scanning ensues by the number of time-consuming angle steps Nφ (or, respectively, Nθ and possibly NΘ) being reduced.
It is a requirement for PPA imaging that the k-space data be acquired not by a single coil, but rather by component coils arranged around the subject linearly, annularly or matrix-like in the form of a two-dimensional acquisition coil array, or cuboid-like, elliptically or spherically in the form of a three-dimensional coil array. As a consequence of their geometry, each of the spatially independent components of the coil array delivers certain spatial information which is used in order to achieve a complete spatial coding by a combination of the simultaneously acquired coil data. This means that, given radial k-space scanning, a number of “omitted” projections in k-space can be determined from a single acquired k-space projection.
PPA methods thus use spatial information that is contained in the components of a coil arrangement in order to replace missing spatial coding (via gradients). The image measurement time is thereby reduced corresponding to the ratio of the number of the partial measurements of the reduced data set to the number of the partial measurements of the complete data set. In a typical PPA acquisition only a fraction (½, ⅓, ¼, etc.) of the partial data sets is acquired in comparison to the conventional acquisition. A special algebraic reconstruction is then applied in order to computationally reconstruct the missing data and thereby to obtain the full field of view (FOV) image in a fraction of the time. The FOV is established by the average interval of the measurement values in k-space.
Known GRAPPA-like PPA methods generate unknown target points from measured source points, with the relative geometric arrangement of these points being fixed. The reconstruction of a number of missing data points occurs by parallel displacement of this basic geometric arrangement (Fourier shift theorem). In particular, an individual measurement value in k-space can be displaced by a specific distance in a specific spatial direction (for example by nΔ k, whereby (n+1) corresponds to the acceleration factor). The calibration (the finding of the coefficients that are necessary for the algebraic reconstruction) typically ensues on the basis of additional calibration measurements in which this same geometric arrangement of source points and target points is repeatedly contained. This is explained using FIG. 2 in the example of a simple three-dimensional Cartesian PPA imaging measurement:
The upper portion of FIG. 2 shows a Cartesian PPA scan orthogonal to the image plane with (for example) a horizontal 3D coding and (for example) a vertical phase coding. Each circle symbolizes a measurement line orthogonal to the image plane, whereby only every third line in the phase coding direction (not to be confused with the measurement line!) is actually measured. Measured measurement lines are shown in the form of filled circles; unmeasured (omitted) measurement lines are shown in the form of unfilled circles. The omission of two respective lines in the phase coding direction effects an acceleration factor of the measurement of n=3. Unmeasured lines can be algebraically reconstructed on the basis of one or more measured lines. A requirement for this is a calibration measurement in at least one partial region of the intended magnetic field in which no lines are omitted (see lower part of FIG. 2). On the basis of such a calibration measurement, an algebraic imaging rule can be found which maps what are known as source lines (right-hatched) to what are known as target lines (left-hatched). The type of the mapping—namely which source lines are mapped to which target lines—conforms with the geometry of the intended, PPA-reduced actual imaging measurement (top of FIG. 2). In the example of FIG. 2, four source lines from four adjacent measured phase coding lines are used for reconstruction of the target lines (horizontal hatching) between the second and the third measured phase coding lines. For clarification, the k-space region involved in the reconstruction is characterized by a boundary in the form of a block. The right-hatched source lines therein form the “support lines” that enable a reconstruction of the horizontally hatched, unmeasured target lines via linear combination. The greater the ratio between the number of the source lines and the number of the target lines, the more exact the result of the reconstruction.
In summary, a block defines a specific imaging rule in order to computationally reconstruct unmeasured k-space lines of an incompletely scanned k-space region corresponding to a PPA imaging. In the following such a block is designated (without limitation of generality) as a “PPA seed” or as a “GRAPPA seed”.
The block or PPA seed in FIG. 2 is symmetrical and extends in total over ten measurement lines in the vertical direction. It has four source lines, each from different adjacent measured k-space lines, so the imaging rule leads only to a reconstruction of the measurement lines between the two average measured lines. By parallel displacement of the block according to FIG. 2 it is therefore possible to complete only the three average unmeasured double rows b, c and d. The PPA seed from FIG. 2 is not suitable for a completion of the rows a and e since it cannot be displaced beyond the shown k-space measurement region. A simple possible PPA seed for completion of the unmeasured border regions a and e would be, for example, a four-line block with a respective source line at the upper end and at the lower end. Such a block, however, represents a limitation with regard to the reconstruction precision since only two source lines are available for reconstruction of paired measurement lines.
It is a disadvantage of existing PPA methods that the calibration measurements require a significant additional measurement effort, in particular given non-Cartesian k-space trajectories.
It is likewise disadvantageous that such imaging or reconstruction rules (conventional PPA seed geometries) cannot be applied or transferred from Cartesian to non-Cartesian scanning trajectories, or can only be applied or transferred in a severely limited manner.